I'm going to tentatively call Kahnei (or Ka'ne or ["ka.nei] or however you want to spell it) a tripartite language, since
Agent,
Direct Object/Theme, &
Experiencer/Indirect Object have different slots in the word order, and there are also particles that mark each. The particles are optional--it's good form to structure your sentences so cleanly that you can leave them out, but if you need them, they're there.
Shisu kimei kelethim: literally [cat] [girl] [I give], would clearly mean "I give the cat to the girl" to most Khanei speakers, since the direct object/theme goes first, the verb/subject/agent goes last, and the recipient/indirect object goes in between.
Being more interested in clarity than notions of austere literary beauty, I personally would probably write:
Shisuanan kimei kelethim, still "I give the cat to the girl," but this time the word for "cat" has been marked with a particle indicating direct-objectness. The final position of "kelethim," and its status as a verb+person marker, pretty unambiguously mark it as the agent of the action. "Lethim" (give) is a ditransitive verb, and "kimei" is the only word left, so that more or less settles "kimei's" status as the receiver/indirect object, even disregarding its medial position.
Attaching any more syntax-particles would start to sound redundant and silly, but that changes if you throw another verb in there:
Shisu u'okopashta kimei kelethim: literally, [cat] [he/she/it is sleeping] [girl] [I give]. Who's asleep here? The cat? The girl? The speaker, who must have some kind of somnambulistic pet-distribution problem? Verbs-as-modifiers don't have a fixed grammatical position, so this is a perfectly grammatical Khanei sentence that is completely confusing. Adding particles that indicate the participants' relationships to each other helps:
Shisuanan a'u'okopashta
ojukimei kelethim: literally, [cat+d.o. marker] [sleeping+abbreviated form of the d.o. marker] [girl+recipient marker] [I give]. "Sleeping" now agrees with "cat," and contrasts with "girl" and "I give." The meaning is therefore, "I give the sleeping cat to the girl."
If you want to get more complicated, you can write:
Shisu u'okopashta kimei u'okolethim tokai: [cat] [he/she/it is sleeping] [girl] [he/she/it is giving] [man]. "Man's" presence at the end of the sentence strongly suggests that it is the subject of the sentence, and most probably its agent, just as "cat's" position strongly suggests it's the d.o. and the theme. Subject and agent need not be the same, however, or this thread would not exist,

and the number of nouns and verbs in this sentence is confusing. It could conceivably mean all kinds of things involving men, sleeping, girls, cats, and giving. It could plausibly be indecent.
You can fix that with particles that positively identify each participant's role:
Shisuanan a'u'okopashta
ojukimei u'okolethim
tokai'iwa: literally: [cat+d.o. marker] [he/she/it is sleeping + d.o. marker] [girl+recipient marker] [he/she/it is giving] [man+agent marker]. Or, "The man is giving the sleeping cat to the girl." "Sleeping" and "cat" must go together, and they're both marked as "direct object." "Girl" is marked as the recipient, which eliminates her from agenthood, and therefore from being the person doing the giving. "He/she/it is giving" can only refer to the noun marked with the agent particle: "man."